An Algorithm for the Numerical Application of a Linear Operator

ABSTRACT

The use of iterative procedures for interpolation is well-known. In this paper an iterative procedure, that may be used to compute values of derivatives and definite integrals, is derived. The procedure may also be used to compute the result of applying any linear operator to a function. The data used are a set of point values, at any reasonable set of abscissae. Within certain limitations, values of the derivatives may also be used. Worked examples are given to demonstrate the use of the procedure in three simple problems.

REFERENCES

• 1: AITKEN, A.C. Proc. Edinburgh Math. Soc. 3(2) (1932), 56-76.
• 2: Begnaud Francis Hildebrand, Introduction to numerical analysis: 2nd edition, Dover Publications, Inc., New York, NY, 1987
• 3: MILNE-THoMPSON, L.M. Calculus of F~nite Differences. Macmillan.
• 4: NEVILLE, E. H. J. Indian Math. Soc. 20 (1934), 87-120.

INDEX TERMS

Primary Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.3 Numerical Linear Algebra
          Subjects: Linear systems (direct and iterative methods)

Additional Classification:
  G. Mathematics of Computing
  G.1 NUMERICAL ANALYSIS
      G.1.2 Approximation
          Subjects: Linear approximation

General Terms:
Algorithms, Measurement, Performance, Theory